[BLANK_AUDIO]. So, now we've developed most of the equations which we need in order to measure rates of reaction. Let's look at some specific examples. And the first one we're going to to look at is where we're using the pressure to follow a, the course of a reaction. And the reaction we're going to consider is the decomposition of N2O5 into NO2 and NO3. We're going to have a pressure increase here. As we're going from one molecule of reactants to two molecules of products. So we can start by writing out a rate expression for this process, so the rate is going to be equal to sum rate constant times the concentration of N2O5 raised to the sum power n, which at the moment we don't know. We're measuring, going to measure pressure changes, so we would like to somehow convert the concentrations, which we need to know, into pressures, and for gases, there is a direct correlation here. So we know that the, the concentration of N2O5 is going to be directly proportional to the partial pressure of N2O5. And therefore, we can reformulate our rate expression into a rate constant. We'll give it a k prime. Give it different rate constant to take into the constant of proportionality. We can now change the concentration into pressure of N2O5, raised to the power n. [NOISE] So what we are actually going to measure in this reaction? So the thing, the easy thing to measure is the total pressure in the reaction. So we follow the reaction and measure the total pressure. What do we know? The information we know. Well, let's start in the reaction we will know the initial pressure of N2O5 if we start only with reactants. So, this is information which is known. So the total pressure, P tot is going to equal the sum of all the pressures of the individual gases. So the pressure of N2O5 plus the pressure of NO2 plus the pressure of NO3. Now, from the stoichiometry of this reaction, we've got one molecule on the left going to two molecules on the right; we can also see that when we produce one molecule of NO2, we'll always be producing one molecule of NO3, and therefore, it must be the case, that the pressure of NO2, must always be equal to the pressure of NO3. Therefore we can rewrite the total pressure P tot now, by inserting for NO, NO3, you can insert NO2 here, and then we end up with the pressure of N2O5 plus pNO2 plus pNO2 so plus two times the pressure of NO2. Okay, now if we also look at the reaction, when we look at the amount of N2O5, which is actually consumed during the reaction, so this is being used up, the N2O5, it starts at a pressure of N2O50, the initial pressure. And if we subtract the pressure it, time T, this will be the amount of this molecule; which is consumed. But for everyone molecule we use up this molecule, we will produce one molecule of NO2, so this must be equal to the amount of NO2 produced must be equal to the pressure of NO2. So therefore, we can write out a new expression for the pressure of NO2, which must be equal to the pressure of N2O5 at the beginning minus the pressure of N2O5 at time T. Okay, well if we now have the pressure of NO2, we can insert that back into the totals pressure. So, and we also have that for the total pressure from this equation here, is going to be equal to the pressure of N2O5 plus two, two times pressure NO2, replace that with this expression here, so pressure N2O5 initial minus pressure of N2O5. So we now have an equation in the total pressure, the pressure of N2O5, and the initial pressure of N2O5. What we're interested in to solve our problem is, we need the pressure N2O5. That's what we're going to use for our concentration of N2O5. So just rearrange this, eventually to give the pressure of N2O5. Rearrange, rearrange this expression, we get two times the initial pressure of N2O5, initial, minus the total pressure. So now we're in the realms of things that we know; this we didn't know; we were trying to get the pressure N2O5. But we know the initial pressure of N2O5. And we are measuring the total pressure, so this is known, and this is known. So we can now proceed using, plotting this function here, twice the pressure of N2O5 minus total pressure. And you can use that instead of the concentration. And if it's a first order plot, for example, we would now plot the log of this function versus time. And that would be for a first order process. [BLANK_AUDIO]